Trace-free Einstein gravity as a constrained bigravity theory

TL;DR

This paper introduces two diffeomorphism-invariant actions for trace-free Einstein gravity, framing it as a constrained bigravity theory where energy-momentum conservation naturally emerges from the equations of motion.

Contribution

The authors present novel actions for trace-free Einstein gravity that incorporate auxiliary fields, establishing a connection to constrained bigravity theories and ensuring conservation laws.

Findings

Two diffeomorphism-invariant actions derived for trace-free Einstein gravity.

Energy-momentum conservation emerges from equations of motion in these actions.

The formulations relate trace-free Einstein gravity to constrained bigravity models.

Abstract

Trace-free Einstein gravity is a prominent alternative to general relativity, which has two versions: one in which the energy-momentum conservation is assumed a priori and another in which it is not. In the first version, the cosmological constant arises as an integration constant. We report two diffeomorphism-invariant actions for trace-free Einstein gravity in which the energy-momentum conservation emerges directly from the equations of motion. The first action is based on the metric, while the second action is based on the tetrad and connection where the conservation of the energy-momentum holds if torsion vanishes. To achieve this, auxiliary fields but otherwise dynamical are introduced in the corresponding actions, which have the form a constrained bigravity theory. These results constitute a significant advance in our understanding of trace-free Einstein gravity.